Effect of heat loss on performance of thin film thermoelectric: A mathematical model

To produce a higher electrical power in thin film thermoelectric legs, one way is to conduct the heat flow in-plane parallel to the surface of thin films. One important advantage of using the thermoelectric element in-plane is that, due to high thermal resistance of the thermoelectric leg, there is no need for an efficient heat sink at cold side. A comprehensive mathematical model for analyzing performance of a ZnSb based thermoelectric thin film is proposed based on one dimensional (1D) steady state analysis. Finite element method is employed to solve governing equations, and effects of temperature dependency of thermoelectric material are considered in the model. The modeling study is carried out by a comparison between the ideal case, where there is no heat loss from the thin film, and the case that the heat loss accrues from lateral surfaces of the thin film to the ambient. By taking side surface heat transfer into account for both vertical and horizontal placement of the thin film, two different nonlinear temperature distributions along the thin film length are obtained, and variation of matched power output versus different thermal boundary conditions is shown. The results show that convective heat transfer to the ambient reduces thermoelectric power output, especially at higher temperature difference between the hot and cold sides of the leg. Furthermore, different parameters such as Seebeck coefficient, temperature, generated Seebeck voltage, heat loss, thermoelectric voltage and current at peak power point are evaluated for vertical and horizontal thin film configurations.